[pianotech] action ratio

[Nicholas Gravagne]

Joe,

You actually DO know this. "Key in", etc. is that portion of an action
component  that represents the effort or activation arm of the lever in
question. The "outs" are the resistance arms. So in broad terms, "key in"
is the front half of the key and the key out is the back "half" from
balance to capstan. Ditto on the whip and shanks. Multiplying the ratios of
the key, whip and shank (each component having its own effort and
resistance arms), as they exist on the left hand side of the equation
yields the action ratio (AR), also referred to as the transmission ratio by
Pfieffer in his books.

I don't know if it shows up in all email clients, but the entire equation
as posted, both left and right hand sides should be shown as as division,
which is to say these also represent ratios. Given that, then the left side
ratio (even though it derives as a product of three ratios) is equivalent
to the right side ratio (even though the right side indicates --- or should
depending on how you see in in the post --- as blow-distance-minus-let-off
(divided by) key-dip-minus-aftertouch).

Since there are so many variables here, there can be no one standard for
aftertouch. So without running a bunch of example numbers right now, let's
say we multiply the three component ratios and the AR works out as 5.8 to
1. Another action might yield 5.58 and so on. However, blow distances and
let-offs do not generally vary much, so these can almost be stated as fixed
constants (say 46mm blow and 2mm let off). Key dips can vary more so, but
again, about 10mm plus or minus.

Thus, given the equation it is clear that the left side must equal the
right side, say 5.8 on the left side must somehow equal 5.8 on the right.
If blow distance is locked in at 46 and let off at 2, then this equals (46
- 2) or 44 . Now if key dip is locked in at 10, then all that is left
unknown is after touch. Some simple algebra yields the unknown after touch
as 2.41mm (0.095"). The formula will now balance since:

(Let side Action ratio) of 5.8 is to1 as the:
(Right side Regulation Parameters) of (46 - 2) to (10 - 2.41) or 44 to
7.58. Thus the right hand and left hand ratios are satisfied at 5.8

Now having said this, note two things at least:

1) given the action ratio (AR) as fixed, which it is, once established one
way or another, the only "fudge-ables" are action regulation parameters.
But regardless of what you do with the regulations, these will always
balance the AR value.

2) the reason there can be no one aftertouch value to fit all situations is
that the ARs from one action to another are not all the same; and so "as
goes the AR, so goes the regulation" (which includes the aftertouch
portion).

And so, Joe, you old curmudgeon and Captain of the Tool Police, I really DO
think you get this <G>

NG

Key out x wippen out x shank out = blow distance - let off

Key in wippen in shank in key dip - after touch



On Sat, Aug 25, 2012 at 8:34 AM, Joseph Garrett <joegarrett at earthlink.net>wrote:

>  And they mean what?! I'll need something a bit stronger, like a good
> single malt!"Key in"??? What does that refer to? Just because some brainiac
> thunk that up, doesn' mean squat unless an explanation is with it imo.<G>
> Joe
>
>
>
> ----- Original Message -----
> *From:* Dale Erwin <erwinspiano at aol.com>
> *To: *joegarrett at earthlink.net;pianotech at ptg.org
> *Sent:* 8/25/2012 8:18:25 AM
> *Subject:* Re: [pianotech] action ratio
>
> These are formulas used by Nick Gravagne , David Stanwood and others to
> determine the overall action ratio. Which is a very useful thing to know.
>  Need some Excedrin now Joe?
>
> *Dale Erwin R.P.T.
> Erwin's Piano Restoration Inc.
> **Mason & Hamlin/Steinway/U.S. pianos
> www.Erwinspiano.com
> Phone: 209-577-8397
> *
>
>
>
>
>
> -----Original Message-----
> From: Joseph Garrett <joegarrett at earthlink.net>
> To: pianotech <pianotech at ptg.org>
> Sent: Sat, Aug 25, 2012 8:03 am
> Subject: Re: [pianotech] action ratio
>
> David said: "One formula for the action ratio has been given as:
>
>
> Key out x wippen out x shank out = blow distance - let off
>
> Key in wippen in shank in key dip - after touch
>
>
>
> Does anyone happen to know what the standard (or minimum) aftertouch is in
> this formula or how it was derived? "
>
> David,
> First of all, I need to know what the hell "key out...." and "key in..."
> means. Have never heard the terms. I suspect if I knew, I'd get a headache
> Joe
>
>
> Joe Garrett, R.P.T.
> Captain of the Tool Police
> Squares R I
>
>
>


-- 
Nick Gravagne, RPT
AST Mechanical Engineering
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